Currently the loot system as I'm aware, has shifted to away from 'looter' as a specialized class and more of 'everyone should loot'. This from how loot level is determined by the highest GS within a party, and is applied to the entire party. Yes, Lucker Looter skill and magazines affect personal looting, but overall this means that on average everyone in the party loots the same.
In your scenario, it wouldn't be an issue unless one party member wasn't looting at all (which is like saying they're not killing zombies, or crafting anything, or harvesting blocks). So a party would roughly have the same stone tool level, and if a player had skilled into Lucky Looter then he would be handing down their old tools until they reached Q6 tools (at which point either each player would have to loot for themselves, upgrade to Iron tier, or be content with Q5 stuff).
I see can players suddenly getting a bunch of Stone Shovels because they don't keep them in their inventory (and thus be annoying to find unneeded duplicates). But as long as most players look at the mechanics, it would feel normal. You get a item you need when you need it and in a reasonable amount of time, and don't get an over abundance of items that you don't want. To be honest, most games have this as a way to help a struggling player and only players that look to exploit game mechanics really abuse it.